Two-dimensional equilibrium configurations in Korteweg fluids
Mathematical Physics
2025-05-29 v1 math.MP
Abstract
In this paper, after reviewing the form of the constitutive equations for a third grade Korteweg fluid, recently derived by means of an extended Liu procedure, an equilibrium problem is investigated. By considering a two--dimensional setting, it is derived a single nonlinear elliptic equation such that the equilibrium conditions are identically satisfied. Such an equation is discussed both analytically and numerically. Moreover, by considering a particular boundary value problem of Dirichlet type, some preliminary numerical solutions are presented.
Cite
@article{arxiv.2505.22026,
title = {Two-dimensional equilibrium configurations in Korteweg fluids},
author = {M. Gorgone and F. Oliveri and A. Ricciardello and P. Rogolino},
journal= {arXiv preprint arXiv:2505.22026},
year = {2025}
}
Comments
15 pages, 16 figures